Research record

Re-Tuned for Decay, Plain Still Trails

Ongoing research. This is an experimental result from active work, not a settled conclusion. The numbers are what we measured and the method is described so you can judge it, but the programme is still running and later experiments may revise what it means.

A note on the language in these records. This is a working laboratory notebook for research into training AI models more cheaply and efficiently, so you will read that an approach did not work, that a result did not hold up, or that one method was worse than another. That is the research doing its job, not a verdict on the engineering we deliver to clients. Ruling an approach out is how the search narrows, and these are the pages that teach us the most: nearly every technique we now rely on came from understanding why something else fell short. Testing our own ideas at least as hard as anyone else's is the point of publishing them. More about this programme and why we run it.

Part of a bigger question: Is the task we are studying actually hard? – Often it is not. A rule from 1990 with no parameters beats the trained model on the task most of these results were measured on, and what an intervention costs is set by the task's own structure.

In plain English

What we asked. With a learning rate that decays over training, our easy-sum mix had beaten ordinary training by a wide margin, but ordinary training was still using settings chosen for a constant rate. We re-tuned it for the decaying schedule.

What we found. Its best setting brought it to 49 percent on the hard sum. The easy-sum mix, on the same schedule, reached 90. Re-tuning closed about a third of the gap.

Why it matters. This was the last check we had planned before writing the result up for outside readers. The claim that survives: on this task, a short start on easier sums reaches the solution in about 40 percent fewer steps than the best ordinary recipe we could find.

The rest of this page is the technical record: the design, every number, and the limits. It is written for a reviewer, and you do not need it to have understood the result above.

New here? How to read a research record
  • Start at the verdict. Every record states, before the experiment was run, what result would have made us abandon the idea. That is the "kill test". Then it says whether the test fired. Nothing gets reinterpreted after the fact.
  • Numbers in square brackets are uncertainty. 23.4 [18.1, 28.7] means our best estimate is 23.4 and the true value is probably somewhere in that range. If a range includes zero, we cannot claim an effect.
  • Results that rule an idea out are kept. Roughly half of what is published here says an approach did not work, including plenty of our own. Those pages are the output, not a shortfall: knowing which direction is a dead end is what lets the next experiment go somewhere better, and most of what we now rely on came out of understanding why something else fell short. Work that only publishes what worked is not measuring anything.
  • Read the Limits section. Every record ends with what it does not show. It is the most honest part of any experiment and usually the shortest.
  • Pro tip: the figures near the top are designed to carry the result on their own. If you read nothing else, read the caption under each one, which says what it shows and what to take from it.
EXPLORATORY. Not a preregistered study. Local CPU, 48 new training runs of 8000 steps plus 32 re-used from A47. The design and the kill test were committed (b648d1f) before any run.

Program v2 Bucket A, item A51. Decisive computation: analysis/sum_decay_tuned.py. Output: analysis/sum_decay_tuned.json.

The question

A47 found that under a cosine-decaying learning rate the early mixture of easier sums beats plain training with a rate warm-up by +0.612 on modular sum -- with the plain arm's peak rate tuned at a constant rate, not for decay. Re-tuned for the decaying schedule, does the plain run close the gap?

Re-tuned for a decaying learning rate, ordinary training still trails
Re-tuned for a decaying learning rate, ordinary training still trails. Ordinary training with a warm-up and a learning rate that decays to zero, at four peak rates, against the easy-sum mix on the same schedule. Error bars are 95% confidence intervals. Given its best peak for this schedule, ordinary training reaches 49%; the mix 90%. Tuning ordinary training for decay closed about a third of the gap, not all of it.

Design: plain (2, 7) with A47's schedule (a 500-step warm-up, then cosine decay to zero at 8000) at peaks 0.005, 0.007 and 0.01; the 0.003 cell and the mixed arm are A47's runs; sixteen of A47's seeds. Kill test, fixed before execution: mixed minus the best decayed plain cell includes zero or lies below it; a best peak at 0.01 is reported as not found. Anchor, in code: the 0.003 cell reproduces A47 on the first seed -- held.

Results

Cell (sixteen seeds, cosine decay)Final (2, 7) accuracySolved (>= 0.9)
plain, peak 0.003 (A47)0.312 [0.107, 0.516]3
plain, peak 0.005 (best)0.491 [0.263, 0.720]6
plain, peak 0.0070.448 [0.243, 0.653]3
plain, peak 0.010.118 [0.056, 0.181]0
easier sums mixed first (A47, peak 0.003)0.897 [0.800, 0.994]12

The kill test does not fire. Re-tuned for the decaying schedule, the plain run's best peak is 0.005, inside the grid; the mixture still beats it by +0.406 [+0.196, +0.616]. Re-tuning closed about a third of A47's gap (+0.612), not all of it. The mixture's own peak was not re-tuned, which if anything favours the plain run.

What it says

The modular-sum result now holds against the best plain recipe found at a constant rate with a warm-up (A40, A44), on a second target (A43, A45), and under a decaying schedule with the plain recipe re-tuned for it (A47, A51). The draft write-up for an outside venue, docs/external/data-curriculum-vs-warmup-draft.md, is marked ready for the maintainer's review.

What stands

  • A51: kill test does not fire. Mixed minus the best decayed plain cell (peak 0.005): +0.406 [+0.196, +0.616]; solved 12 against 6.

Limits

  • Sixteen seeds; four peaks, one ramp, cosine only; the mixture's schedule untuned for decay.

Terms on this page

Every piece of vocabulary this record uses, in plain language. Generated from the text above, so it cannot drift out of step with it.

accuracy
The fraction of answers a model gets right on questions it was not trained on.
curriculum
Training on easier examples first and harder ones later, like a school syllabus, rather than on everything at once.
kill test
A condition written down before running the experiment that says what result would make us abandon the idea. Fixing it in advance is what stops a disappointing result being reinterpreted as an encouraging one.
learning rate
How big a step training takes each time it updates the model. Too small and nothing happens; too big and it never settles.
seed
The number that fixes all the randomness in a training run. Same seed, same run. Running several seeds is how you tell a real effect from a lucky one.

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